RW-PINK-0612 / Rainbow / Review draft

Chapter 31 F-080 - Spreadsheet capacity gate Exact expression

Terminology revised · evidence inherited

Rainbow Pages Combined 1351 Pages. Source pages 8396-8396. Nomenclature updated; historical equations, evidence limits and unresolved relationships retained.

RW-PINK-0612
Chapter 31 F-080 - Spreadsheet capacity gate Exact expression
official-docs/pink-paper/volumes/PinkPaper_Volume03_Formulas_F051_F100.pdf
NODE PLACEMENT / RAINBOW PATH
N1
N2
N3
N4
N5
N6
N7
N8
N9
Primary situational anchor: N1; U/D/C remain profile-specific.
R STATUS / OBSERVATION
R preserves pre-observational or anticipated state. R1 records an identified but
unresolved living observation. N1 is the first prediction-based admission node.
R2 may be emitted only after evidence, physics, proof, authority, and
claims-ceiling gates pass.
SOURCE RULE / INTENT
Pink source PinkPaper_Volume03_Formulas_F051_F100.pdf, page 65 of 106.
Chapter 31 F-080 - Spreadsheet capacity gate Exact expression
lambda_total<=rho_max*sum_p(mu_p) AND
memory_required<=memory_available AND
cross_partition_edges<=cut_limit↪ Meaning.
Admissionrequiresthroughput,memory,andpartition-boundarycapacitytopasstogether.
Bound manifestations.MK,JO,M3,SISTER,MJOS Gateway
stage.Bangel.beginworkbookdeclaration,JPmodel,MKcost,JOdeterministicexecution
Construct Formula-specific expr
PATH OF EXPRESSION
Human purpose -> MJ scope -> Bangel typing -> Elsa semantic recovery -> JP representation -> MK physics classification -> JO proof -> Angels/Bellatrix/Sister/EVE
evidence -> M3 routing -> Mermaid/Shiva when applicable -> MJ bounded decision -> JO evidence.
CODE / MATH / PROCESS REPRESENTATION
module MJ.Rainbow.Chapter_31_F_080_Spreadsheet
reference "PINK-04-P0065"
state R -> R1
node N1
representation JP(PINK-04-P0065)
physics MK(classify, units, boundary, uncertainty)
verify JO(types, evidence, receipts)
if all_required_gates == PASS:
MJ.permit -> R2 -> bounded_output
else:
HOLD | FAIL_TECHNICAL | DENY
# Pink source PinkPaper_Volume03_Formulas_F051_F100.pdf, page 65 of 106. Chapter 31 F-080 - Spreadsheet capacity gate Exac
Internal reference only. No physical validation, operation authority, product certification, external effect, IP approval, or ethics waiver.
MJ-PBMEF-DAY0-R12-RAINBOW-230K-PDF-MIRROR-FINAL | RW-PINK-0612

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